Properties of branes in curved spacetimes

TL;DR

This paper explores how branes positioned at focal points in curved spacetimes exhibit unique properties, including supersymmetry and dualities, with detailed analysis in AdS and plane wave backgrounds.

Contribution

It demonstrates that branes at focal points in curved geometries have special properties, including supersymmetry and duality, with explicit examples and detailed string analysis.

Findings

AdS_2 branes at poles are half supersymmetric and dual to monopoles in SYM.

Branes at focal points exhibit flat-space-like amplitudes.

String modes become massless at focal points, affecting amplitudes.

Abstract

A generic property of curved manifolds is the existence of focal points. We show that branes located at focal points of the geometry satisfy special properties. Examples of backgrounds to which our discussion applies are AdS_m x S^n and plane wave backgrounds. As an example, we show that a pair of AdS_2 branes located at the north and south pole of the S^5 in AdS_5 x S^5 are half supersymmetric and that they are dual to a two-monopole solution of N=4 SU(N) SYM theory. Our second example involves spacelike branes in the (Lorentzian) plane wave. We develop a modified lightcone gauge for the open string channel, analyze in detail the cylinder diagram and establish open-closed duality. When the branes are located at focal points of the geometry the amplitude acquires most of the characteristics of flat space amplitudes. In the open string channel the special properties are due to stringy modes that become massless.